A common parameter for describing the accuracy of a weapon is the circular probable error, generally refer red to as CEP. CEP is simply the bivariate analog of the probable error of a single variable and measures the radius of a mean centered circle which includes 50% of the bivariate probability mass. In the case of circular normal errors where the error variances are the same in both directions, CEP can be expressed in terms of the common standard deviation, and estimators are easily formulated and compared. In the case of elliptical normal errors, CEP cannot be expressed in closed form, and hence, estimators are less easily formulated. The problem addressed herein is the comparison of CEP estimators for the elliptical case based on some of the commonly used CEP approximations.